Conventional flexures for supporting a proof mass in an accelerometer are generally formed of ceramic oxides such as silicate glasses (silica), crystallized glasses (lithium aluminum silicate) and crystalline solids (sapphire, quartz). These materials are preferred because of their low hysteresis and low anelastic response. However, there are certain problems associated with these flexures, primarily their susceptibility to stress fractures. This is particularly apparent in flexures which contain a pattern of cuts or holes in the flexure plate in order to increase the flexibility. In such cases the stress concentrations at the cuts and/or at the junctions of elements formed by the cuts and/or holes lead to early stress-related failure. A second problem is that the deflection of the flexure introduces non-linearity in the response and the greater the deflection the greater the non-linearity of the response. This consequently limits the range over which a particular accelerometer can operate and requires increased data processing to compensate for the non-linearity.